A finite element method for a model of population dynamics with spatial diffusion
Milner, F.
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Milner, F.
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Li, Yu, Lin, Qun, Xie, Hehu
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In this paper, we present a parallel scheme to solve the population balance equations based on the method of characteristics and the finite element discretization. The application of the method of characteristics transform the higher dimensional population balance equation into a series of lower dimensional convection-diffusion-reaction equations which can be solved in a parallel way. Some numerical results are presented to show the accuracy and efficiency.
Villanueva, Rafael J., Arenas, Abraham J., González-Parra, Gilberto (2008)
Journal of Applied Mathematics
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Gerardo-Giorda, Luca
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We study a numerical method for the diffusion of an age-structured population in a spatial environment. We extend the method proposed in [2] for linear diffusion problem, to the nonlinear case, where the diffusion coefficients depend on the total population. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. We provide stability and convergence results and we illustrate our approach with some numerical result. ...
Eberl, Hermann J., Demaret, Laurent (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Dehghan, Mehdi (2003)
Mathematical Problems in Engineering
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Claire Chainais-Hillairet, Jian-Guo Liu, Yue-Jun Peng (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We introduce a finite volume scheme for multi-dimensional drift-diffusion equations. Such equations arise from the theory of semiconductors and are composed of two continuity equations coupled with a Poisson equation. In the case that the continuity equations are non degenerate, we prove the convergence of the scheme and then the existence of solutions to the problem. The key point of the proof relies on the construction of an approximate gradient of the electric potential which allows...